Yes, women are more sensitive to high-pitched sounds than men.
Several studies (summarized here) have found that women are better than men when it comes to hearing acuity above 1 or 2 kHz:
Corso (1959) was among the first to report that females have superior
auditory acuity (i.e. lower thresholds) compared with same-age males,
particularly for test frequencies above 2 kHz. The same general
finding – adult females having more sensitive hearing at high
frequencies, compared with same-age males – has been replicated in
other studies of adults (e.g. Chung, Mason, Gannon, and Willson, 1983;
Royster, Royster, and Thomas, 1980), including studies with
Caucasian, African-American, and Asian adults (Dreisbach and
colleagues, 2007; Shahnaz, 2008).
At the same time, the decline in hearing acuity differs between men and women, with men having an earlier onset (already detectable by 30 years of age). The portion of this paper that's behind a paywall (and is not copy-paste-able) says that the biggest difference in losing hearing sensitivity between men and women is in the range between 3 and 4 kHz. In other words, as they age, women lose the ability to distinguish sounds of different frequencies more slowly than men, and this gender difference in speed of decline is the greatest for high frequencies.
In this first paper I linked, it is mentioned that women have lower thresholds in terms of sound intensity as well, i.e. they will be able to hear softer sounds than men. The second paper mentions that it might also be true that men are more sensitive to low-pitched sounds than women. In conclusion, speaking in a lower register actually might help not wake her up, but speaking more softly is also preferable :) Whether this has anything to do with crying babies is a different question.